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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>Consider</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
y^{\prime \prime}+b y^{\prime}+c y=0.
\end{equation*}
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<p class="continuation">The characteristic equation:</p>
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\begin{equation*}
r^2+b r+c=0.
\end{equation*}
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<p class="continuation">We consider the case <span class="process-math">\(b^2-4 c=0\text{,}\)</span> i.e., there are two repeated roots: <span class="process-math">\(r_1=r_2=-\frac{b}{2}\text{.}\)</span> One solution is <span class="process-math">\(y_1=e^{-\frac{b}{2} x}\text{.}\)</span><dfn class="terminology">How to find another linear independent solution? (Reduction of order)</dfn></p>
<span class="incontext"><a href="sec3_5.html#p-102" class="internal">in-context</a></span>
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